### Table 3: Family of valid inequalities for model B

1998

"... In PAGE 11: ... The k-SEC are inequalities that eliminate #5Ccycles quot; #28in the precedence sense#29 for any k-job subsequence. These are shown in Table3 , where B ij and U i are de#0Cned as before. 4 Separation Algorithms For a given class of valid inequalities, the associated separation problem can be stated as follows: Given a point#16x 2 R p satisfying a certain subset of constraints, and a family F of SDST #0Dowshop... ..."

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### Table 3: Impact of valid inequalities on data set one.

2007

"... In PAGE 29: ...1 Impact of valid inequalities The purpose of this section is to investigate the impact of the valid inequalities on the two set partitioning relaxations. Table3 reports results obtained by running the algorithm on the first data set. The table shows results for the SP1 and SP2 relaxations.... ..."

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### Table 7. Lower bounds on ICE small for classes of valid inequalities

2004

"... In PAGE 20: ... In any of these runs, we held up to 1000 valid inequalities in the pool, in every iteration up to 100 inequalities could have been added, and after every iteration, weak cuts were deleted, if the cutting plane pool was full. Table7 presents average and extremal values for the lower bounds of the re- ned LP relaxations, when only one type of cuts has been added. Notice that we only add cycle inequalities in their original formulation (10) to strictly fundamental cycle bases.... ..."

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### Table 2 Impact of the valid inequalities on data set 1.

"... In PAGE 25: ... Tables 2 and 3 show the impact of adding violated valid inequalities. Table2 contains results for the first data set (randomly generated instances), while Table 3 contains results for the TSPLIB instance proposed by Renaud et al. [2002] (second data set).... In PAGE 25: ... The results show that the GOC and GLSEC are the inequalities that work best toward closing the integrality gap. For the first data set ( Table2 ) the LSEC, PSC and StEnC also turn out to be worthwhile. For the second data set (Table 3) the StEnC are less powerful while DGOMC, LSEC, GLSEC, PSC appear to be roughly equally important.... ..."

### Table 3 Impact of the valid inequalities on data set 2.

"... In PAGE 25: ... Tables 2 and 3 show the impact of adding violated valid inequalities. Table 2 contains results for the first data set (randomly generated instances), while Table3 contains results for the TSPLIB instance proposed by Renaud et al. [2002] (second data set).... In PAGE 25: ... For the first data set (Table 2) the LSEC, PSC and StEnC also turn out to be worthwhile. For the second data set ( Table3 ) the StEnC are less powerful while DGOMC, LSEC, GLSEC, PSC appear to be roughly equally important. It is interesting to note the behavior of the DGOMC on the second data set.... ..."

### Table 8: Impact of valid inequalities on a subset of instances.

2007

"... In PAGE 31: ...1 that tested the effect on the lower bound in the root node. The results of this experiment are shown in Table8 . The table contains three major columns.... ..."

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### Table 1: Strength of TSP inequalities. Class of inequalities Strength Ref.

"... In PAGE 2: ... In Section 3, we formally describe a measure to compare two polytopes and show how it can be used to compare various relaxations of the TSP. The results summarized in Table1 are established in Section 4 and interpreted in Section 5. Finally, we conclude with some remarks in Section 6.... ..."

### Table 1. Candidate Values for Inequalities

1999

"... In PAGE 5: ... In addition to the equality operators, numerically typed properties may be involved in inequality expressions of the following form. lt;property gt; lt;inequality gt; lt;value gt; For various inequality operators, Table1 shows how to cal- culate elements to add to the candidate set. MaxPlayers is... In PAGE 7: ...1, lines 27-29). It can also occur by applying Table1 to the predicate at A.4, line 19.... In PAGE 8: ... This can be accomplished in two ways: (1) by reducing the number of candidate values as- sociated with properties and (2) by more quickly recogniz- ing infeasible assignments. A simple optimization of the first kind concerns the selection of values for inequalities as described in Table1 , where we were given a numeric inequality of the following form. lt;property gt; lt;inequality gt; lt;value gt; In response to these inequalities, we added lt;value gt; 1or lt;value gt;+1 as candidate values for the specified property.... ..."

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### Table 1. Candidate Values for Inequalities

1999

"... In PAGE 5: ... In addition to the equality operators, numerically typed properties may be involved in inequality expressions of the following form. lt;property gt; lt;inequality gt; lt;value gt; For various inequality operators, Table1 shows how to cal- culate elements to add to the candidate set. MaxPlayers is... In PAGE 7: ...1, lines 27-29). It can also occur by applying Table1 to the predicate at A.4, line 19.... In PAGE 8: ... This can be accomplished in two ways: (1) by reducing the number of candidate values as- sociated with properties and (2) by more quickly recogniz- ing infeasible assignments. A simple optimization of the first kind concerns the selection of values for inequalities as described in Table1 , where we were given a numeric inequality of the following form. lt;property gt; lt;inequality gt; lt;value gt; In response to these inequalities, we added lt;value gt; 1or lt;value gt;+1 as candidate values for the specified property.... ..."

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